Connection of multiplicative/relative perturbation in coprime factors and gap metric uncertainty

Automatica

Volumn 34, Issue 5, 1998, Pages 603-607

  Gu, Guoxiang ^a   Qiu, Li ^b  

^a LOUISIANA STATE UNIVERSITY   (United States)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Coprime factorization; Gap metric; Robust stability; Uncertain linear systems

Indexed keywords

CONTROL SYSTEM ANALYSIS; OPTIMAL CONTROL SYSTEMS; PERTURBATION TECHNIQUES; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY;

COPRIME FACTORS; GAP METRIC UNCERTAINTY;

LINEAR CONTROL SYSTEMS;

EID: 0032070008     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(97)00186-6     Document Type: Article

References (13)

1. Georgiou, T. T. (1988). On the computation of the gap metric. System Control Lett., 11, 253-257.
2. Georgiou, T. T. and M. C. Smith (1990). Optimal robustness in the gap metric. IEEE Trans. Automat. Control, 35, 673-685.
3. Georgiou, T. T. and M. C. Smith (1992). Robust stabilization in the gap metric: controller design for distributed systems. IEEE Trans. Automat. Control, 37, 1133-1143.
4. Gu, G. (1995). Model reduction with relative/multiplicative error bounds and relations to controller reduction. IEEE Trans. Automat. Control, 40, 1478-1485.
5. McFarlane, D. C. and K. Glover (1990). Robust Controller Design Using Normalized Coprime Factor Plant Descriptions. Springer, Berlin.
6. p gap perturbations. In Proc. European Control Conference, pp. 1020-1025.
7. Qiu, L. and E. J. Davison (1992). Feedback stability under simultaneous gap metric uncertainties in plant and controller. Systems Control Lett., 18, 9-22.
8. Sefton, J. A. and R. J. Ober (1993). On the gap metric and coprime factor perturbations. Automatica, 29, 723-734.
9. Stewart, G. W. and J. G. Sun (1990). Matrix Perturbation Theory. Academic Press, San Diego.
10. Treil, S. (1994). A counterexample on continuous coprime factors. IEEE Trans. Automat. Control, 39, 1261-1263.
11. Vidyasagar, M. (1985). Control System Synthesis: A Factorization Approach. The MIT Press, Cambridge, MA.
12. Vinnicombe, G. (1993). Structured uncertainty and the graph topology. IEEE Trans. Automat. Control, 38, 1371-1383.
13. Zames, G. and A. K. El-Sakkary (1980). Unstable systems and feedback: the gap metric. In Proc. 16th Allerton Conf., pp. 380-385.